Justification of an asymptotic expansion at infinity
نویسنده
چکیده
A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.
منابع مشابه
Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions
A Pick function of d variables is a holomorphic map from Πd to Π, where Π is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series ∑∞ n=1 ρnz −n with real numbers ρn that gives an asymptotic expansion on non-tangential approach regions to infinity. In 1921 H. Hamburger characterized which sequences {ρn} can occur. We give an extension ...
متن کاملAsymptotic expansion for the models of nonlinear dispersive, dissipative equations
Considered herein are the family of nonlinear equations with both dispersive and dissipative homogeneous terms appended. Solutions of these equations that start with finite energia decay to zero as time goes to infinity. We present an asymptotic form which renders explicit the influence of the dissipative, dispersive and nonlinear effect in this decay. We obtain the second term in the asymptoti...
متن کاملWidth of Shape Resonances for Non Globally Analytic Potentials
We consider the semiclassical Schrödinger operator with a well in an island potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginary part of the shape resonance at the bottom of the well. This is a generalization of the result by Helffer and Sjöstrand [HeSj1] in the globally analytic case. We use an almost analytic extension in order...
متن کاملAsymptotic Behavior of Generalized Eigenfunctions in N-body Scattering
In this paper an asymptotic expansion is proved for locally (at infinity) outgoing functions on asymptotically Euclidian spaces. This is applied to N-body scattering where the two-body interactions are one-step polyhomogeneous symbols of order −1 or −2 (hence long-range and short-range respectively). The asymptotic behavior of the N-body resolvent applied to Schwartz functions is thereby deduce...
متن کاملExistence and Uniqueness of v-Asymptotic Expansions and Colombeau’s Generalized Numbers
We define a type of generalized asymptotic series called v-asymptotic. We show that every function with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic expansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness of t...
متن کامل